T-Level Unit 5 Session 16

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

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‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

5. Essential science for engineering and
manufacturing

5.7 Fluid dynamics in engineering

PowerPoint 10: Hydrostatic pressure

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Objectives

By the end of this session, learners should be able to:

•Explain what is meant by hydrostatic pressure and centre of pressure.

•Calculate hydrostatic pressure.

•Calculate hydrostatic thrust on an immersed plane surface.

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Hydrostatic pressure is defined as

“The pressure exerted by a fluid at equilibrium at any point of time due
to the force of gravity”.

Hydrostatic pressure is proportional to the depth measured from the
surface as the weight of the fluid increases when a downward force is
applied.

The fluid pressure can be caused by gravity, acceleration or forces
when in a closed container. Consider a layer of water from the top of
the bottle. There is the pressure exerted by the layer of water acting
on the sides of the bottle. As we move down from the top of the bottle
to the bottom, the pressure exerted by the top layer on the bottom
adds up.

Hydrostatic pressure

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Hydrostatic pressure formula

The formula used to calculate hydrostatic pressure is:

p = ρ g h

where,

p is the pressure exerted by the liquid in N.m-2or Pa

ρ is the density of the liquid in kg.m-3

g is the acceleration due to gravity taken as 9.81m.s-2

h is the height of the fluid column in m

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Depth of Water

Pressure

Ft

M

Pa

Bar

1

0.30

2943

0.03

5

1.52

14911.2

0.15

10

3.05

29920.5

0.30

15

4.57

44831.7

0.45

Hydrostatic pressure vs depth of water

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Next >

The pressure in a fluid
does not depend on factors
like the surface area of the
container, the mass of the
liquid, or its volume.

Liquids in an open
container always have the
same height in every part
of the container –
regardless of its shape.

A communicating vessel- the height of fluid is
the same in each part of the vessel.

The behaviour of fluid

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Centre of pressure

Hydrostatic force is the resultant force acting on a submerged surface
due to the pressure loading of the fluid into which the surface is
submerged.

Centre of Pressure

The location of the hydrostatic force is the centre of pressure. The centre
of pressure is always below the centre of gravity of the surface in
contact.

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Hydrostatic thrust acting on an immersed surface

The thrust force acting on a surface submerged in a
liquid can be calculated as:

F = pa A =ρ g A x

where

F = thrust force (N)
pa = ρ g ha = average pressure on the surface (Pa)
A = area of submerged surface (m2)
x = average depth (m)
ρ = density (kg/m3) (water 1000 kg/m3)
g = acceleration of gravity (9.81 m/s2)

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

Example - the thrust force acting on the side of a
container

The trust force acting on the submerged vertical side of a container
can be calculated as:

F = pa A

= ((pt + pb) / 2) A = (ρ g (ht + hb) / 2) A

where
pt = pressure at the top of the submerged surface (Pa)
pb = pressure at the bottom of the submerged surface (Pa)
ht = depth at the top of the submerged surface (m)
hb = depth at the bottom of the submerged surface (m)

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T Level Technical Qualification in
Engineering and Manufacturing (Level 3)
300 Engineering Common Core Content

© 2022 City and Guilds of London Institute. All rights reserved.

‘T-LEVELS’ is a registered trade mark of the Department for Education.
‘T Level’ is a registered trade mark of the Institute for Apprenticeships and Technical Education

The thrust on a surface with width 1 m and height from 0 m to 2 m in
a water-filled container can be calculated as

F = (ρ g (ht + hb) / 2) A

= (1000 kg/m3) (9.81 m/s2) ((0 m) + (2 m)) / 2) ((1 m) (2 m))

= 19620 N

= 19.6 kN

Example (continued)

Open Ended

Worksheet 10: Hydrostatic pressure

Divers must be careful when working at depth in water and need to carefully control the dissolving of gases in their blood stream.

 

Calculate the pressure created by a 30 m depth of water given the density of water is 1000 kg/m³ and gravity 9.8 N/kg.

Open Ended

Worksheet 10: Hydrostatic pressure

The density of sea water is ~1025 kg/m³, the maximum depth of the Atlantic Ocean is ~8500 m (8.5 km).

 

Calculate the water pressure at this depth.

Open Ended

Worksheet 10: Hydrostatic pressure

At a depth of 12.5 m of a chemical solvent the pressure at the bottom of the storage tank due to the solvent was 306 kPa

Calculate density of the solvent.